• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1233-1242
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• 2009

In 1981 S. A. Saxon and P. P. Narayanaswami ([10]) showed that every (LF)-space has an infinite dimensional separable quotient. In this note we prove that this fails for (LF)$_{tv}$-spaces. We construct a wide class of (LF)$_{tv}$-spaces, which have no infinite dimensional separable quotient.